CAJ | 학술논문

为了研究平行球面s7的代数结构,引进了Hopf拟群上的拟模和双拟模代数的概念,由于这些概念的公理中模缺少结合性的条件,通过增加对极的条件来弥补结合性的条件.并通过双拟模代数构造了扭曲冲积的概念,事实上这种扭曲冲积是Hopf代数上扭曲冲积的推广,并且证明了扭曲冲积与张量余积成为Hopf拟群的充要条件为当且仅当下列条件(h1→a)(x)h2=(h2→a)( )h1,(a←S(h1))(x)h2=(a←S(h2))(x)h1成立.所得到的结果推广并改进了Hopf代数上扭曲冲积一些相应的结果.
위료연구평행구면s7적대수결구,인진료Hopf의군상적의모화쌍의모대수적개념,유우저사개념적공리중모결소결합성적조건,통과증가대겁적조건래미보결합성적조건.병통과쌍의모대수구조료뉴곡충적적개념,사실상저충뉴곡충적시Hopf대수상뉴곡충적적추엄,병차증명료뉴곡충적여장량여적성위Hopf의군적충요조건위당차부당하렬조건(h1→a)(x)h2=(h2→a)( )h1,(a←S(h1))(x)h2=(a←S(h2))(x)h1성립.소득도적결과추엄병개진료Hopf대수상뉴곡충적일사상응적결과.
In order to study algebraic structures of parallelizable sphere s7,the notions of quasimodules and biquasimodule algebras over Hopf quasigroups,which are not required to be associative,are introduced.The lack of associativity of quasimodules is compensated for by conditions involving the antipode.The twisted smash product for Hopf quasigroups is constructed using biquasimodule algebras,which is a generalization of the twisted smash for Hopf algebras.The twisted smash product and tensor coproduct is turned into a Hopf quasigroup if and only if the following conditions ( h1 →a) (x)h2 =(h2→a) (x)h1,( a.←S( h1 ) ) (x)h2 =( a←S( h2 ) ) (x )h1 hold.The obtained results generalize and improve the corresponding results of the twisted smash product for Hopf algebras.